4.2.2—Complex loci

|z−a|<r selects the interior of a circle and |z−a|>r its exterior. An argument inequality selects a wedge, with boundary rays included or excluded according to the sign.

Test one convenient point to decide which side of each boundary is wanted, then combine conditions. State whether boundaries are included.

|z|≤2 and arg z between 0 and π/2 gives a closed quarter-disk in the first quadrant.

Sketching only the boundary is incomplete when an inequality describes a region.